Sensors which rely on the interference between two waves, typically two orthogonal polarization modes of a wave, are known and used in a wide range of technical fields. The detector signals of these sensors are related to the cosine of the relative phase shift ϕ between the two waves. Therefore, phase shifts of ϕ and ±ϕ+2nπ (n being an integer number, also referred herein as the period counter) produce the same interference output, and hence cannot be distinguished from one another. Consequently, the unambiguous measurement range of the relative phase shift is limited to a range of [0, π].
For example, an electro-optic DC voltage sensor consisting of a bismuth germanate (Bi4Ge3O12, or BGO) crystal with its [001] crystal axis oriented along the optical path of the waves (see also reference [1] for further details) has a corresponding π-voltage or an unambiguous measurement range of about 75 kV for light waves at 1310 nm.
Although the sign ambiguity (between ϕ and −ϕ can be removed by combining two polarimetric signals with a (static) relative phase offset (preferably π/2, called quadrature signals) as described for example in ref. [2], the periodwise ambiguity (between ϕ and ϕ+2nπ) is an inherent problem for all interferometric measurements.
For relative measurements of phase shifts, the measurement range can be extended by fringe counting, zero-counting or similar history-tracking techniques. In AC voltage measurements, one can thus extend the measurement range to many times the π-voltage by combining quadrature polarimetric signals and using zero-counting (see ref. [2-4]), facilitated by the fact that the AC voltage continuously oscillates about zero. However, for absolute measurements in which history information is either unavailable or unreliable, the periodwise ambiguity is a genuine problem and places a fundamental limit to the achievable measurement range. This is particularly the case for DC voltage or DC current measurements, due to the absence of an oscillating waveform and thus the lack of a zero reference. Furthermore, the latter makes it difficult to distinguish voltage or current drifts from other effects such as changing optical loss, stress-induced birefringence, etc. It has been attempted, see ref. [5], to address the drift problem by chopping the applied voltage, but such solutions are not readily adaptable to HV applications.
Electro-optic voltage sensors can also be built using the modulation phase detection (MPD) technique as described for example in [6]. It is generally implemented in a non-reciprocal phase modulation scheme and commonly used in fiber-optic gyroscopes and fiber-optic current sensors, see ref. [7, 8]. Reciprocal MPD sensors have excellent phase accuracy and DC stability. The co-owned Patent U.S. Pat. No. 7,911,196 (cited herein as reference [9]) describes a voltage sensor incorporating a voltage sensing element (or several such elements), a 45° Faraday rotator, and the MPD modulation and detection electronics. The periodwise ambiguity remains a limitation in this technique, and therefore the sensor as described is also only capable of measuring a DC electro-optic phase shift ϕ between −π and +π. A similar system with a transverse-configuration voltage cell can be found in ref. [10].
There have been efforts to extend the unambiguous measurement range of interferometry beyond 2π. Both patent applications WO9805975A1 [11] and EP1179735A1 [12] propose for example using two distinct optical wavelengths, particularly in an electric voltage or current measurement. Because the optical phase shift as induced by the measurand depends on the wavelength, the interferometric signals measured at the two wavelengths generally have different periodicities as a function of the measurand. Hence, the measured value pair consisting of detector readings at the two wavelengths does not have a simple periodic dependence on the measurand, and can therefore be used to unequivocally allocate the measurand value in a large range. Three or more wavelengths can also be used (see ref. [12]), providing further advantages of eliminating all remaining ambiguous points. The two-wavelength (or multi-wave-length) method, however, requires at least two sets of light sources and detectors at distinct wavelengths, which significantly add to the complexity and may reduce the reliability of the sensor system.
In another approach in interferometry, low-coherence light is used. Such radiation encompasses a relatively broad bandwidth (sometimes known as white light), as opposed to the monochromatic radiation emitted by coherent laser sources, which are used in conventional interferometers. Consequently, the coherence time of the low-coherence light, inversely proportional to the band-width, is relatively short, equal to only a small number of optical periods. Low-coherence light sources are widely used in many fiber sensors, especially those consisting of many disparate sections, components and interfaces, mainly to temporally localize interfering waves and eliminate spurious interference from undesired back-scattering and cross-coupling. The same idea is also explored in coherence-multiplexed sensor systems as described in [13], where multiple signals are combined and separated based on their non-overlapping coherence times.
The narrow coherence peak provides a natural absolute reference for interferometric measurements. One of the earliest attempts to employ this principle for a sensor application appeared in ref. [14], and the first fully developed position sensor was demonstrated in [15] and U.S. Pat. No. 4,596,466 [16]. A number of low-coherence interference sensors have been developed using the same principle, to measure physical quantities such as pressure [17], temperature [18, 19], etc. Typically in these systems, a remote sensing interferometer is optically connected to a local reference interferometer in series. The low-coherence light produces a packet of white-light interference fringes as the local interferometer is scanned (either mechanically or electronically as described for example in reference [20]), and the central fringe in the packet provides an absolute reference for the accurate reproduction and locking of the phase shift between the two interferometers, so that no “zero-forgetting” should occur after an interruption. The local interferometer is simultaneously interrogated to measure the transferred phase shift, e.g., with another monochromatic light by fringe counting. It should be noted that for all the techniques using low-coherence light sources as described above, the low-coherence light is used to unambiguously transfer the interference signal from one interferometer to another, and the phase measurement is carried out in the reference interferometer by conventional fringe-counting means.
A related optical ranging technique termed optical coherence-domain reflectometry is also known, see ref. [21, 22]. The technique scans a delay line and detects the white-light interference fringes in order to measure the arrival times of the reflected waves from various interfaces. It was commercialized in the early 1990s and has gained widespread use in the field. The same concept can be extended to surface profiling [23], and also to cross-sectional imaging in biological samples, in which case an entire field called optical coherence tomography (OCT) [24] has emerged, which has become a very powerful tool in biological diagnostics. These techniques use the reflected or scattered white-light interference fringes for sample characterization. For these techniques, the phase shift of the waves used is generally not a parameter of interest.
Instead of scanning the delay to obtain white-light interference fringes in what is known as the time-domain approach, one can alternatively vary the detection wavelength and measure the spectrum at a fixed non-zero delay, in a so-called frequency-domain approach. In this case, one measures a modulated spectrum containing many spectral fringes. The frequency-domain white-light interferometry contains basically the same information as the time-domain counterpart, and the data acquisition can be accomplished in a single shot by a spectrograph. It is widely used in optical coherence tomography research [25] but has also seen some sensor applications.
In Patent U.S. Pat. No. 5,301,010 [26], the dependence of the white-light interference fringe contrast on a physical quantity is explicitly used to measure that quantity. In this patent, a dual-interferometer setup is used and the reflector in one arm of the reference interferometer is oscillated back and forth to record a number of white-light interference fringes about a given position. The value of the interference contrast at the given path length is calculated using the relative intensities of the maxima and minima of these fringes, and the measurand is then inferred from the contrast value. A preferred embodiment with a stepped mirror is also included in this patent, producing two shifted white-light interference fringe packets with the measurement point located in between. In this patent, the interference contrast is calculated and deliberately used for the measurement of a physical quantity. However, no phase measurement is performed in this technique, and scanning through multiple interference fringes is required to measure the contrast.
WO 94/18523, WO 03/093759 and US 2006/0158659 describe interferometric setups that also rely on scanning the whole interference fringes of broadband light.
In the light of the above, it is seen as an object of the invention to provide an interferometric sensor with the parameter to be measured represented by a relative phase shift between two waves, which does not exhibit periodwise ambiguity. It is seen as a particular object of the invention to remove periodwise ambiguity for sensors measuring DC parameters which do not oscillate rapidly during the duration of a measurement.